\documentclass[12pt]{article}
%\usepackage{pandora,euler}
\usepackage{graphicx,fullpage,amsmath,amsfonts}

\begin{document}

\title{Math, Mind, and Music}
\author{Quiz 3}
\date{April 15, 2005}
\maketitle

% \vspace*{\fill}
% {\baselineskip=40pt
% \begin{tabbing}
% Student ID Number: \= \kill
% Last Name: \> \rule[-2pt]{10cm}{0.3pt} \\
% First Name:  \> \rule[-2pt]{10cm}{0.3pt} \\
% Signature: \> \rule[-2pt]{10cm}{0.3pt} \\
% %% Code: \> \fbox{\rule{0pt}{1.5em}\rule{1.5ex}{0pt}}
% %% \fbox{\rule{0pt}{1.5em}\rule{1.5ex}{0pt}}
% %% \fbox{\rule{0pt}{1.5em}\rule{1.5ex}{0pt}}
% %% \fbox{\rule{0pt}{1.5em}\rule{1.5ex}{0pt}}
% \end{tabbing}}


% \vspace*{\fill}
Solve 3 out of four questions for a 100\% score.  Extra credit is
possible.

% \vspace*{\fill}

% \newpage



\begin{enumerate}

\item
\begin{enumerate}
\item Define rhythm.
\item What is cross rhythm?
\item What is the relationship between duration and intensity of
sound?
\end{enumerate}
\hfill (1+2+2)

%\newpage

\item We discussed psychological experiments to quantify the
perception of rhythm.
\begin{enumerate}
\item What stimuli are used when investigating rhythm in simple
psychological experiments?
\item What is the dependent variable in these experiments?
\item What tasks have the participants to perform? (Describe two.)
\end{enumerate}
\hfill (2+1+2)
%\newpage

\item Music happens on vastly separate time scales.  Indicate typical
durations (or ranges of durations) for each of the following.
\begin{enumerate}
\item Shortest repetition time such that two tones are perceived as
separate
\item Natural beat interval that humans choose without external
stimuli
\item Length of a single rhytmic pattern in music
\item Length of a musical phrase
\item Length of a single piece of music
\end{enumerate}
\hfill(5)

%\newpage

\item Find and name as many symmetries as you can in the following
excerpt of a piece by Webern.  \hfill(5)
\end{enumerate}
\begin{center}
\includegraphics[width=14cm]{webern2.pdf}
\end{center}


\end{document}

\section*{Solutions}
